50 citations · 193 across the 27 of their papers we have counts for
12 papers · 1 filter
The Barron-Lipschitz Energy Gap and Depth Separation Phenomena in Scientific Machine Learning
Nima Rezaei, Stephan Wojtowytsch
We illustrate in several examples that even neural networks of infinite width (specifically, Barron functions) may encounter substantial obstacles when used as a model class for pr…
Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs
Oluwatosin Akande, Patrick Dondl, Kanan Gupta +2
We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine le…
A note on spatially inhomogeneous Cahn-Hilliard energies
Stephan Wojtowytsch
In 2023, Cristoferi, Fonseca and Ganedi proved that Cahn-Hilliard type energies with spatially inhomogeneous potentials converge to the usual (isotropic and homogeneous) perimeter…
Some observations on high-dimensional partial differential equations with Barron data
Weinan E, Stephan Wojtowytsch
We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such funct…
Connected Coulomb Columns: Analysis and Numerics
Patrick Dondl, Matteo Novaga, Stephan Wojtowytsch +1
We consider a version of Gamow's liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in…
On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime
Stephan Wojtowytsch
We describe a necessary and sufficient condition for the convergence to minimum Bayes risk when training two-layer ReLU-networks by gradient descent in the mean field regime with o…
On the motion of curved dislocations in three dimensions: Simplified linearized elasticity
Irene Fonseca, Janusz Ginster, Stephan Wojtowytsch
It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetriz…
Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields
Patrick Dondl, Matteo Novaga, Benedikt Wirth +1
We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional…
The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip
Patrick W. Dondl, Matthias W. Kurzke, Stephan Wojtowytsch
We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model consists of a Peie…
On the Boundary Regularity of Phase-Fields for Willmore's Energy
Patrick Dondl, Stephan Wojtowytsch
We demonstrate that Radon measures which arise as the limit of the Modica-Mortola measures associated to phase-fields with uniformly bounded diffuse area and Willmore energy may be…
Uniform Regularity and Convergence of Phase-Fields for Willmore's Energy
Patrick Dondl, Stephan Wojtowytsch
We investigate the convergence of phase fields for the Willmore problem away from the support of a limiting measure . For this purpose, we introduce a suitable notion of essenti…
Phase field models for thin elastic structures with topological constraint
Patrick W. Dondl, Antoine Lemenant, Stephan Wojtowytsch
This article is concerned with the problem of minimising the Willmore energy in the class of \emph{connected} surfaces with prescribed area which are confined to a small container.…